Using distance on the Riemannian manifold to compare representations in brain and in models

An Explainable Geometric-Weighted Graph Attention Network for Identifying Functional Networks Associated with Gait Impairment

One of the hallmark symptoms of Parkinson's Disease (PD) is the progressive loss of postural reflexes, which eventually leads to gait difficulties and balance problems. Identifying disruptions in brain function associated with gait impairment could be crucial in better understanding PD motor progression, thus advancing the development of more effective and personalized therapeutics. In this work, we present an explainable, geometric, weighted-graph attention neural network (xGW-GAT) to identify functional networks predictive of the progression of gait difficulties in individuals with PD. xGW-GAT predicts the multi-class gait impairment on the MDS-Unified PD Rating Scale (MDS-UPDRS). Our computational- and data-efficient model represents functional connectomes as symmetric positive definite (SPD) matrices on a Riemannian manifold to explicitly encode pairwise interactions of entire connectomes, based on which we learn an attention mask yielding individual- and group-level explainability. Applied to our resting-state functional MRI (rs-fMRI) dataset of individuals with PD, xGW-GAT identifies functional connectivity patterns associated with gait impairment in PD and offers interpretable explanations of functional subnetworks associated with motor impairment. Our model successfully outperforms several existing methods while simultaneously revealing clinically-relevant connectivity patterns. The source code is available at https://github.com/favour-nerrise/xGW-GAT.

Multitask representations in the human cortex transform along a sensory-to-motor hierarchy

Human cognition recruits distributed neural processes, yet the organizing computational and functional architectures remain unclear. Here, we characterized the geometry and topography of multitask representations across the human cortex using functional magnetic resonance imaging during 26 cognitive tasks in the same individuals. We measured the representational similarity across tasks within a region and the alignment of representations between regions. Representational alignment varied in a graded manner along the sensory-association-motor axis. Multitask dimensionality exhibited compression then expansion along this gradient. To investigate computational principles of multitask representations, we trained multilayer neural network models to transform empirical visual-to-motor representations. Compression-then-expansion organization in models emerged exclusively in a rich training regime, which is associated with learning optimized representations that are robust to noise. This regime produces hierarchically structured representations similar to empirical cortical patterns. Together, these results reveal computational principles that organize multitask representations across the human cortex to support multitask cognition.

Revisiting Riemannian geometry-based EEG decoding through approximate joint diagonalization

Objective.The wider adoption of Riemannian geometry in electroencephalography (EEG) processing is hindered by two factors: (a) it involves the manipulation of complex mathematical formulations and, (b) it leads to computationally demanding tasks. The main scope of this work is to simplify particular notions of Riemannian geometry and provide an efficient and comprehensible scheme for neuroscientific explorations.Approach.To overcome the aforementioned shortcomings, we exploit the concept of approximate joint diagonalization in order to reconstruct the spatial covariance matrices assuming the existence of (and identifying) a common eigenspace in which the application of Riemannian geometry is significantly simplified.Main results.The employed reconstruction process abides to physiologically plausible assumptions, reduces the computational complexity in Riemannian geometry schemes and bridges the gap between rigorous mathematical procedures and computational neuroscience. Our approach is both formally established and experimentally validated by employing real and synthetic EEG data.Significance.The implications of the introduced reconstruction process are highlighted by reformulating and re-introducing two signal processing methodologies, namely the 'Symmetric Positive Definite (SPD) Matrix Quantization' and the 'Coding over SPD Atoms'. The presented approach paves the way for robust and efficient neuroscientific explorations that exploit Riemannian geometry schemes.

Geometric learning of functional brain network on the correlation manifold

The correlation matrix is a typical representation of node interactions in functional brain network analysis. The analysis of the correlation matrix to characterize brain networks observed in several neuroimaging modalities has been conducted predominantly in the Euclidean space by assuming that pairwise interactions are mutually independent. One way to take account of all interactions in the network as a whole is to analyze the correlation matrix under some geometric structure. Recent studies have focused on the space of correlation matrices as a strict subset of symmetric positive definite (SPD) matrices, which form a unique mathematical structure known as the Riemannian manifold. However, mathematical operations of the correlation matrix under the SPD geometry may not necessarily be coherent (i.e., the structure of the correlation matrix may not be preserved), necessitating a post-hoc normalization. The contribution of the current paper is twofold: (1) to devise a set of inferential methods on the correlation manifold and (2) to demonstrate its applicability in functional network analysis. We present several algorithms on the correlation manifold, including measures of central tendency, cluster analysis, hypothesis testing, and low-dimensional embedding. Simulation and real data analysis support the application of the proposed framework for brain network analysis.

Caveats and Nuances of Model-Based and Model-Free Representational Connectivity Analysis

Brain connectivity analyses have conventionally relied on statistical relationship between one-dimensional summaries of activation in different brain areas. However, summarizing activation patterns within each area to a single dimension ignores the potential statistical dependencies between their multi-dimensional activity patterns. Representational Connectivity Analyses (RCA) is a method that quantifies the relationship between multi-dimensional patterns of activity without reducing the dimensionality of the data. We consider two variants of RCA. In model-free RCA, the goal is to quantify the shared information for two brain regions. In model-based RCA, one tests whether two regions have shared information about a specific aspect of the stimuli/task, as defined by a model. However, this is a new approach and the potential caveats of model-free and model-based RCA are still understudied. We first explain how model-based RCA detects connectivity through the lens of models, and then present three scenarios where model-based and model-free RCA give discrepant results. These conflicting results complicate the interpretation of functional connectivity. We highlight the challenges in three scenarios: complex intermediate models, common patterns across regions, and transformation of representational structure across brain regions. The article is accompanied by scripts (https://osf.io/3nxfa/) that reproduce the results. In each case, we suggest potential ways to mitigate the difficulties caused by inconsistent results. The results of this study shed light on some understudied aspects of RCA, and allow researchers to use the method more effectively.